| Where Recherche duTemps Perdu|
---- meets Kirchliche Dogmatik
Who's on Second; What's on First. One of the fascinating consequences of the special theory of relativity concerns the sequence of events. More accurately it leads us to the conclusion that under certain circumstances, observers may see some events in reverse order. Did A come before B, or did B come before A?
Let me state right now that the theory of relativity does not allow time travel, visions into the future, or an effect preceding its cause. We may have to come back to those points if necessary.
What the theory does lead us to conclude is that different observers may see certain events in different sequences. There's nothing particularly spooky about that. We are used to the fact that people may hear sounds at different times because sound has a definite speed. For example, if you were to set up a sound system for a large theater, you would have to take into account that there will be a lag in the time between the speech an actor makes on stage and when the people in the last row hear it.
Once again, the matter hinges on the two givens of relativity theory: there is no privileged point for absolute observations, and the speed of light is constant.
Again, even though I can think of lots of my own illustrations (and you probably can as well, at least when we're done here), I'm going to borrow one from Atkins, Physics (471-74), so that I can feel secure that I'm not just running away with my imagination. Needless to say, I'm still telling the story itself in my own way.
Let's bring out once again our intrepid rocket scientists, Jeff and Tony. Today Jeff has decided to do an experiment involving a sequence of flashing lights. To this end, he acquired a long metal girder, made sure that he had identified its exact center, and suspended it with precision below his spaceship. When you're dealing with the speed of light, accuracy is imperative. At each end he mounted a packet of explosive material that will, upon ignition, give up an extremely bright momentary light. In the meantime, Tony is hovering in his own space ship a good distance away.
In the diagram, J stands for Jeff, T for Tony, M indicates the middle of the pole, and the lights are installed at points P and Q. When Jeff pushes a button, he triggers two rays of light that move in opposite directions from the center M to the ends at P and Q. When they reach the packets, they will set off the explosions, and both of our adventurers will keep track of when they see the lights.
Since Jeff sits equidistant from the packets, he will notice the two lights flashing simultaneously.
But not so Tony. Due to his position in relationship to P and Q, he is going to see the explosion at P before the one at Q. Here is how it will appear to him:
Now Jeff decides to make things more interesting. He adds a third exploding packet to the beam at point R, a little closer to the center than Q. The same impulse will trigger the new flash to go off.
What Jeff will see is the explosion at R, followed by the simultaneous explosions at P and Q.
What will Tony see? If he is stationed properly, which he must since this is a thought experiment, his sequence will be: first P, then R, and then Q. So, like Jeff, he sees R before Q. But he sees P before R, while Jeff saw R before P. Thus, the frame of reference determines which event has been observed prior to another one.
By my constantly qualifying the subject matter to the effect that it is all about observations and perceptions, hopefully you see that there is nothing illogical here. You have a contradiction or inconsistency when two statements cannot both be true at the same time in the same sense. Clearly, statements by or about the perceptions of Tony and Jeff do not fulfill the requirement for having the same sense because they come from different frames of reference. Furthermore, "at the same time" has taken on a whole new meaning in this context.
But, just for fun, let me add another part of this scenario as Atkins actually presented it and amplify it somewhat. In his version, the explosions at the ends of the beam are triggered by the rays of light caused by a small explosion at M.
Now, I am going to add the stipulation that this explosion is also visible to both investigators, but I'm not going to insert animations for this part because what I'm going to do with it is not possible. On this hypothesis, Jeff's sequence of observations would be M, R, and then both P and Q simultaneously. So far, so good. Tony's sequence, on the other hand, would be P, M, R, Q. Aha! There's the hiccup: The event at M caused the event at P. But then, if Tony saw P before M, he actually would have observed an effect before its cause.
However, that cannot happen, and not just on the grounds of philosophical dogma. If the light from an explosion at M caused the explosion at P, then we cannot forget about the time that the light took to travel from M to P where it set off P's explosion. Thus, there is a built-in time lag that cannot be overcome. Necessarily, since we're talking about the speed of light, Jeff's steel girder must be extremely long so that all of the explosions don't appear to have occurred simultaneously to any observer. And, if that's the scale we're having to work with, it should be evident that the distance between M and P must be long enough so that Tony cannot see M before P. (In the pure abstract reality, the scale does not matter.)
The point is clear, I hope. The principle of relativity describes the universe in such a way that different people have different perceptions about some hypothetical sequences of events. But the fundamental order of existence, in this case the necessary succession of causes and effects, is left intact.
We had more snow again today! And the long-range forecast predicts some more next week. I'm sorry I'm stuck on the weather, but--then again--we're stuck with what we're getting. I wish I had more to report, but our lives are rather quiet at the moment. My studies are really focused on the physics stuff at the moment as well as some other things that I can't mention now, which are due to appear on the web eventually. Before going back to relativity, let's have one more lesson from Luke.
Well, I spoke (or wrote) a little too soon. Something happened, and it's definitely not a big deal compared to all the current troubles in the world, but it bothers me. In the process of writing this entry, while maintaining the energy necessary for the task by consuming a chocolate chip cookie for fuel, I broke one of my front teeth. I'm really unhappy about that. I already had a dentist appointment scheduled for next Monday anyway, but now it's going to be a whole lot more complicated, I assume. Furthermore, I'm going to be unbelievably self-conscious if I have to talk to anybody over the next week.
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v. 13: Then He laid His hands on her, and instantly she was restored and began to glorify God.(HCSB)
In this passage, the leader of a synagogue takes umbrage with the fact that Jesus healed a woman on the Sabbath. Apparently the location, i.e. in the synagogue, was not an issue, but the timing definitely was. Let's walk through the story and make some observations along the way.
Jesus was teaching in a synagogue. It was customary to give prominent teachers who visited a synagogue the opportunity to address the congregation, and Jesus did so. I imagine that in the audience were many of the "regular crowd" (cue Billy Joel) that was following Jesus around, as well as a number of folks whose main motivation may have been pure curiosity. The building was most likely pretty filled.
We don't know the content of what Jesus was teaching on that particular Saturday. Perhaps it was some of the material preceding this passage in Luke, which would explain why this story is situated in this section of the gospel. As Jesus was looking over the people in the audience, he saw a woman who was badly hunched over and could not straighten herself. A spirit (demon) was doing this to her. The text does not specify whether she had come deliberately to be exorcised or healed. However, when Jesus saw her he called out to her, "Woman you are free of your disability!" Then, as our lead verse informs us, "he laid hands on her and began to glorify God."
This scenario deserves some reflection apart from the issue that was subsequently raised. I have mentioned the fact that Luke brings up the interaction of Jesus with women more often than the other gospel writers. What strikes me is that the woman was right there, visible in the congregation. Maybe at this time synagogues did not yet practice the separation of men and women, or at least not as rigorously as some orthodox synagogues do to this day.
No sooner had Jesus performed this act of healing, than the leader of the synagogue publicly reproved, not Jesus, but the people in the crowd for coming to be healed on the Sabbath. The direct scolding was directed at the people, but by implication also at Jesus for doing the healing. It was a violation of the Sabbath in the leader's mind.
Jesus responded to him harshly. "You are hypocrites," he told them, clearly referring to the leader and others who might have agreed with him. We can't say for sure at this point that they were Pharisees, although it is likely, given the information I will cite below. As we've seen several times, a number of Jewish teachers at the time were building the so-called "fence" around the Law, which meant that they were deliberately over-interpreting the Law in the strictest possible manner so that, if anyone were to break it, they would only violate the human interpretation rather than God's Law itself.
To go on with the point Jesus was making. They were hypocrites, he said, because at the same time as they were interpreting the Law in a burdensome manner for people, they were giving themselves exemption to care for their livestock. They had declared that it was permissible to untie donkeys or oxen to give them water. So, Jesus said in a rhetorical master stroke (and I paraphrase a little bit): Here is someone who is not just an animal, but a human being; not just a human being, but a special one, namely, a daughter of Abraham. Surely if it's legitimate to untie an ox from its physical restraint, it must be all the more legitimate to loosen the spiritual bonds besetting this woman.
The crowd cheered, and the leader was embarrassed.
Was it really a violation of the Law to heal someone on the Sabbath? There's nothing in the Old Testament that supports this view. However, could it have been a violation of the rabbinic teachers' interpretation of the Law (the "fence")? Indeed, it was, and it is stated as such in the Talmud, the collection of interpretations of the Law that was finally finished in the 5th century AD. The Talmud consists of a number of tractates. The tractate called Shabbat, section 109, makes that very point, as explained by Rabbi Adam Chalom on his blog, Not Your Father's Talmud, in which he provides humanistic interpretations and critiques of the Talmud. He makes the good point that "if we think in terms of professional healers, it makes more sense – even doctors are allowed a day off!" But the matter went further than that.
We cannot always be sure whether the rules given in the Mishna and the Talmud already applied in all the specifics in the first century, but the reference to this rule in Luke indicates that it was at least seminally practiced already. The Talmud actually goes much further than prohibiting healers to pursue their profession on the Sabbath. Also excluded are the personal administration of herbs or other healing substances to oneself. As laid out in Shabbat 109 one may eat various herbs and drink various liquids (obviously within the usual dietary limits), as long as they do not have medicinal value. If the intent is to provide healing for the person, the item is off the menu for the day. No later than the Mishna (3rd cent. AD), any active measures that would promote healing were considered wrong on the Sabbath.
Now please let me reiterate what I usually say in contexts such as this one: If one believes that their spiritual state depends on the most meticulous observance of God's Law, this is not just clever hairsplitting. One can be very sincere and pious in attempting to please God with one's actions. Still, if it comes down to treating animals better than humans, my personal opinion (insofar as I may be entitled to one) is that the letter of the interpretation is no longer in tune with the spirit of the Law as God gave it. And, even though I just said it is possible to be sincere in adhering to the Law, the words of Jesus here leave little doubt that for the most part the interpretations revealed a great amount of hypocrisy. Finally, let's be clear that what we are looking at here is not intrinsically a problem with Judaism. Legalism is a well-known phenomenon in Christianity as well.
Several commentators make the point that this passage is not about the person of Jesus, but about the keeping of the Sabbath. That assessment may be true with regard to the details of the incident. As mentioned above, the leader of the synagogue rebukes the congregation, not Jesus. Nevertheless, it strikes me that this distinction is pretty artificial. After all, it was Jesus who healed the woman and countered the leader's scolding. And, regardless of whether it is stated explicitly here or not, it is clearly the case that one cannot read this passage without realizing that Jesus frees us from the burden of the Law.
It is Ash Wednesday, by the way. If you must observe Lent, please do so by celebrating the fact that Christ has already done everything that is necessary for your salvation. Inspect your life if you feel compelled to do so. Come to terms with your sins as the Holy Spirit may guide you. But these things apply anytime throughout the year. Leave your issues with Christ and be joyful. If you can't be joyful at this moment, please at least don't exacerbate your burdens by putting yourself into a special framework geared toward depression. "Lent" is not taught in the Bible, and neither you nor God profit from any unnecessary deprivations on your part. If you cannot go through these next few weeks without some kind of special recognition, let it be on the miracle of God's grace.
We've not given Luke his turn in several posts, so it's definitely time to return to the Bible passage. (I have the next entry on relativity laid out in my mind already, but it'll have to wait. In the meantime, you can go to the entire collection, including the latest additions by clicking here. You don't need to scroll down to find the various entries.)
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v. 9: Perhaps it will bear fruit next year, but if not, you can cut it down. (HCSB)
God is patient.
As always when we read a parable, please keep in mind that we should not treat it as an allegory, in which each detail is a symbol or metaphor with an exact counterpart in some literal biblical concept. Looking over various commentaries and websites, there is a tendency to try to find symbolic meanings in the various components of the story, but it leads to some real complications: Israel is sometimes represented as a grape vine. At other times she shows up as a fig tree. So, maybe we can say that the vineyard is Israel, and the fig tree is its leadership? That's a little bit of clever inventiveness, but has no grounding in the text.
Another common interpretation is that God is the owner of the vineyard, with Christ playing the role of the gardener. I can't buy that identification either in light of the fact that the Son and the Father are not on two different sides towards us. Let's forget about finding symbolic meanings and just read the passage as a parable. The function of parables is to strengthen particular points, and we go out on a pretty long limb when we try to find more in them than their main point. Which is in this case: God is patient.
Having said that, I also need to add that there's nothing wrong with looking at the details just to see how the parable makes its point.
We start with a fig tree in a vineyard. What's a fig tree doing in a vineyard? Grapevines are fairly demanding plants, and it would seem intuitively weird to plant trees in their vicinity because they will withdraw the water and the nutrients that the grapes need. It is, of course, possible that Jesus was deliberately providing an absurd setting in order to catch his audience's attention, but there's no need to posit such a scenario (see the addition below). We also cannot rule out that the term "vineyard" may have been used in the more general sense of "garden." However, the overwhelming majority of commentators state that it was a common practice in the time of Jesus to plant certain kinds of trees right next to grapevines. Presumably, even though they may have provided competition for water, they also released other nutrients into the soil from which the grapevines benefited. Thus, a fig tree in a vineyard does not represent take us into surreality.
[Insert on 3-5-2014] It took me a bit of searching on the web, but I didn't want to reference the source below until I had some clear evidence in hand. The Rev. James Richardson, against whom I have nothing except that he teaches his congregation without due prior preparation, proclaimed in a sermon posted on his blog, Fiat Lux, that "no one – but no one – plants a fig tree in their vineyard." If that's supposed to mean planting a fig tree right in the middle of the vines, he is right of course, but neither Jesus nor his listeners nor the vintners of the day would have been so silly as to do that. The trees would have been on the edge of the garden. And I hereby present you with a picture of a vineyard in the area of Puglia, a region in Italy, together with fig trees. The picture was taken by a gentleman who apparently goes only by the name of "Fabio" on his weekly bike tour of the countryside of vineyards and olive trees of publia. [End of insert. Continue below the picure. ]
The agricultural proprietor went to inspect the tree to see if was bearing any fruit. He had been doing so for three years, and there still wasn't any. That would make the tree at least six years old. Yeah, I've gotten so inspired by the physics entries that I can't avoid adding a little math here as well. Here's the relevant portion from Leviticus 19:23-25:
|When you come into the land and plant any kind of tree for food, you are to consider the fruit forbidden. It will be forbidden to you for three years; it is not to be eaten. In the fourth year all its fruit must be consecrated as a praise offering to the Lord. But in the fifth year you may eat its fruit. In this way its yield will increase for you; I am Yahweh your God.|
We see then that according to the Law of God, one should not expect any fruit on any newly-planted tree, and then in the fourth year, any fruit would go to God as a praise offering. Only from its fifth year on, was one allowed to eat its fruit. Commentators come up with different numbers, but it seems to me that if the owner had been looking for fruit for three years, the minimum age for the tree had to have been six. On that basis, we can also infer that the man did not want to eat the figs himself, but offer them to God in the prescribed manner.
Unfortunately for the fig tree, the lengthy wait wasn't doing the owner any good, which meant that it didn't do it any good for itself either. In case you're wondering, figs are dioecious, which means that there are male trees and female trees. The pollen is communicated between flowers by insects, e.g., wasps. So, the lack of fruit could be due to the absence of female trees or the right kind of wasp in the vicinity. The owner would not have been able to consult Google to find out whether fig trees were dioecious, as your inquisitive bloggist did, and blamed the tree. "It's not doing any good, just sapping the good soil. Time to uproot it."
But the vineyard worker wasn't ready to give up on the tree. "Please, sir, let me give it one more year. I'll dig a ditch around it and give it lots of extra fertilizer. If that won't do the trick, I won't have any objections to getting rid of it." The gardener was speaking fairly authoritatively to the owner; the latter must have trusted him.
None of this has anything to do with the interpretation of the parable. I've brought them up because 1) I was wondering about the details behind the parable myself; and 2) I wanted to clarify that Jesus wasn't relating absurdities in this parable.
The parable followed right on the heels of Jesus' response to certain Jews who were passing judgment on the apparent sinfulness of others, as supposedly demonstrated by the fact that they underwent suffering. Jesus said that they were no more guilty than others, and that no one was exempt from the need to repent. And then he told the parable, which provided pretty much the same message, but also emphasizing that any delay is an extension for our benefit so that we still have time to respond to God's call. God is patient.
God's patience manifests itself in many different ways. What comes to my mind first of all is his patience with me. I don't need to go into any details; I know my weaknesses. You know yours, and God is patient with you as well.
I do need to clarify a couple of more points while we're in this neighborhood. I've heard preachers and evangelists add impetus to their invitations by saying that God calls on people to respond to him only once or twice in their lives. "If God is speaking to you right now, come forward and accept Christ. This may be your last opportunity." Obviously our opportunities to come to Christ are limited by the length of our lives and possibly other circumstances, but the idea that God has a put a numerical limit on his offer of salvation is not biblical.
On the other hand, God's patience is not indulgence. God is patient in calling people to repentance, belief, and trust in Jesus and his work, but, as mentioned above, there is a limit. It is not the one claimed by some revival preachers, but it's still there. The atheist who challenges God to strike him with lightening to demonstrate his existence will receive the answer he asked for, just on a different time schedule. These are hard words, but they are also a part of the message of this parable.
How does relativity slow down clocks?
I’ve phrased the question in a way that actually already embeds any number of misconceptions. However, judging by some Q&A sites on the web, it’s apparently the way that any number of folks have been led to think of the phenomenon. Here are some necessary qualifications.
• Relativity doesn’t do anything. It’s not some kind of entity exerting causal power, but a concept that arises out of an analysis of the manner in which we need to interpret certain observations of the world.
• The interpretation does not say anything about clocks in general. It’s about observing one or more clocks outside of one’s own frame of reference. Your own clock, presuming that it’s not defective, is always correct. (The German Uhr is a little bit more helpful in this case because it does not distinguish between “watch” and “clock.” Any accurate time-keeping device is fine, though we'll use a really unusual one in a few moments.)
• Speaking of being picky about the language we use, let me guard what I’m saying a little bit more. Strictly speaking, Einstein did not say that there could not be an ether or other absolute frame of reference, but he said that it was superfluous and rejected it as playing any role in our understanding of the motion of bodies. (“On the Electrodynamics of Moving Bodies,” 1).
Up to now I have left the distinction between Galilean relativity and Einstein’s special theory of relativity somewhat blurred. Let me state the difference now succinctly. Atkins, (Physics, 450) defines the classical (i.e. Galilean and Newtonian) principle of relativity as
The fundamental laws of physics are independent of the velocity of the observer.
For Einstein’s special theory of relativity we can go to the man himself (“On the Relativity,” 4). His version includes two principles. The first one is pretty much the same as the Galilean version, just expressed with more technical language. The second one is the addition of the constancy of the speed of light.
1) The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion. [“Uniform translatory motion” refers to the supposition that the systems do not change velocity. If they accelerate the principle becomes a whole lot more complex. That eventuality will be encompassed by the “general theory of relativity.]
2) Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body. Hence
So let us illustrate this idea with an example, based on Einstein’s own paper, but with your creative bloggist’s slight reworking of the details. First of all, I’m going to just “talk” you through this thought experiment. Then, for those who are interested, I’ll try to specify the math involved in describing the result.
Imagine that there are two scientists, call them Jeff and Tony, at the controls of two spaceships. They are able to communicate with each other. For purposes of this example it is not necessary that they would be flying anywhere near the speed of light. Each of them has a clock on board, and each of them can see his own clock as well as the other’s clock.
Now, when I say clock, I’m not thinking of the apparatus that we usually call a clock (e.g., a watch, a grandfather clock, a wall clock, etc.), though, again, any of them would theoretically work as long as they’re not defective, but would not be as suitable for a direct explanation of this topics. The clocks we have in mind are rods, each one exactly one meter long, and each one of them sporting a light-emitting source on the bottom end as well as a mirror on the top and one on the bottom. The source emits a beam of light that hits the upper mirror and reflects it down to the lower mirror. Since the speed of light is a constant, this back-and-forth oscillation will always take exactly the same time in any inertial system. We'll call the amount of time it takes for the light to make one up-and-down trip a “tick.” Quantitatively, a tick is the time that it takes for light to move up and down one meter for a total of two meters or 200 cm.
Now, let’s say that Tony remains stationary and observes his own clock. Throughout this experiment his clock never changes. The light beam travels up and down consistently following its vertical path of 2 meters, with each up-and-down stroke constituting a tick.
Then he looks over at Jeff’s rocket. Jeff’s clock functions in the same way: The time of one up and down sequence by the beam along the rod constitutes one tick. However, because Jeff's system is in motion, Tony does not see the light pursuing a neat up-and-down path on Jeff’s pole. Keep in mind the earlier illustration of what an outside observer sees when a ball is tossed up in the air on a moving train. Similarly, the movement of the light takes place in a more complex manner. As it moves up and touches the upper mirror, Jeff’s spaceship has already moved a certain amount, and the same will be true when the light returns to the bottom mirror. At each interesting juncture, Jeff's frame of reference has moved along a short distance. So, what Tony sees is a triangle-like configuration for the light beam. Just by looking at a drawing of the scenario, we can see that Tony’s light has had to travel farther than Jeff’s within the time span of one tick. Even if the angle at the midpoint is a whole lot steeper than I have drawn it, an angle is there.
Consequently, one or the other must be true:
Either Jeff's light beam traveled faster than Tony’s in order to complete its movement, or Jeff’s tick was longer than Tony’s in order for the light beam to complete its motion in the span of one tick.
Well, the speed of light is constant, and so we have to discard the option of the light speeding up. Thus, we are left with the other alternative. Since the light had to travel a longer distance on Jeff’s space ship than on Tony’s in one tick, Jeff’s tick must last longer than Jeff’s. Therefore, Jeff’s clock runs somewhat slower. How much longer Jeff’s tick is, compared to Tony’s, obviously depends on how fast he is moving with respect to Tony.
At least that’s what Tony observes. If the roles were reversed, and Jeff’s frame of reference were stationary while Tony was zipping along, Jeff would observe that Tony’s clock was slower than his for the same reason. It comes down to who examines the other one’s clock. In each person’s own frame of reference the tick is going to be 200 cm divided by the speed of light, while in the observation of the other’s it’s going to be a little longer than that.
To summarize, since the beam of light is observed to go through a greater length in one system than in the other, and since the length of time is defined by the time it takes for the beam of light to complete its path, the clock outside of the observer’s frame of reference will be found to be slower than the observer's in order to accommodate the additional distance the beam of light had to traverse.
Okay, let’s look at the math, which in this section of Einstein’s paper is comparatively manageable, though my math never comes with a guarantee of being mistake-free. Once again I’m following Atkins (467-69) pretty closely.
Tony’s system is stationary, his rod is exactly 100 cm long, and the speed of light is about 3x1010 cm/sec. We apply the equation
t=l/c = 200cm/c.
So the up and down journey of the light is 2x102 cm divided by 3x1010 cm/sec, which works out to 2/3x10-8 seconds, or better 6.7x10-9 seconds. That’s the length of the tick in Tony’s immediate environment: 0.0000000067 seconds. Now let’s look again at what Tony sees on Jeff’s clock. Jeff’s spaceship is moving along at a velocity, for which we can’t give it a number, but just simply call v.For our present purposes, light travels in straight lines. Let’s call the point where the beam originates A, the point where it makes contact with the upper mirror B, and the point where it makes contact with the lower mirror C. We’ll refer to a “tick” simply as time, abbreviated as t.
We want to know how much longer Jeff’s tick is compared to Tony’s, and to arrive at that conclusion, we'll leave behind the pictures of rockets and just think of the geometry of the path of light as a triangle.
There is no justification for supposing that any of the angles are right angles, but we can bisect the triangle at point B and refer to the midpoint between A and C as D. Then the angle at D is a right angle, and we can do some good old trigonometry.
We know that the line BD is exactly 100 centimeters long. The hypotenuse is line AB. So, we can formulate the other two lengths algebraically, since we know that in each case the length it took the light to move along that line is ½ t. So, the length of AB is one half of a tick multiplied by the speed of light.
The ship’s velocity is not the speed of light; we can only give it the generic variable v. We can say that the length of AD is one half tick multiplied by the velocity of the rocket.
Now we can bring out the Pythagorean Theorem according to which
and substitute the more complex formulas we just came up with:
(½ tc)2 = (½ tv)2 + 1002
Subtracting (½tv)2 from both sides we get
(½ tc)2 – (½ tv)2= 1002
A fundamental rule of algebra is that whatever you do to one side, you have to do to the other. But that applies only if we do something that changes the values. We can rearrange one side of an algebraic equation as long as it still says the same thing. So, we can factor out ½ t from the left side and derive
¼ t2(c2-v2) = 1002
Let’s get rid of that silly fraction by multiplying both sides by 4.
t2(c2-v2) = 4x1002
Next, we’ll divide both sides by (c2- v2):
t2 = 4 x 1002
We happen to know that (4x100)2 = 2002, so we can write:
t2 = 2002
And if we factor out c2 from the bottom of the fraction we get:
t2 = 2002
Now, all we need to do is take the square root of both sides and we arrive at our goal (more or less):
t = 200
(The square root sign is supposed to cover the entire expression (1-v2/c2). Now if we want to express the length of a tick on Jeff's clock as seen by Tony, we can express it as a ratio, in which we can ignore (or set as "1") the vertical length and get:
That's the length of a tick on Jeff's clock according to Tony's frame of reference. We don’t know the number for v, but we are allowed to assume that there are no imaginary numbers involved. Therefore the denominator of that fraction is less than 1, and the total value of the fraction is larger than 1. Therefore, time has expanded or, to put it the other way around, Jeff's clock appears to be slow.
When we get back to this series, we’ll investigate what happens to sequences of events when vehicles travel in the vicinity of the speed of light.
Just to get it out of the way, in case you’re interested, winter is still solidly ensconced here in Indiana. The forecast includes some temperatures at or below 0°F, and the mother of all snow and ice storms is supposed to be starting late tonight. It just will not quit. Always winter--though we did have Christmas.
The last few days were doctor visit days, Dr. N, the gastroenterologist, on Wednesday and Dr. W, the movement disorder specialist, on Thursday. Everything went fine.
I’ve been doing a lot of writing and erasing trying to present the theory of relativity in such a way that it is both understandable and correct. Please let me know (nicely) if you see any mistakes. And please remember that this is not an essay in physics per se, but that I’m stating my take on developments in physics and whatever impact they may or may not have on a Christian world view.
It seems as though much, if not most, of what follows hangs on the constancy of the speed of light, 3 x 1010 cm/sec in empty space. You may wonder why the speed of light is so important. That’s because this is not a course in physics, and so we haven’t dealt with much of what would precede this material in a physics textbook. Let me put it this way: If you read casual articles on science, you may see statements along the line of: Quantum mechanics becomes crucial on the level of the tiniest entities, such as atoms and subatomic particles, while relativity becomes an important factor when investigating enormous speeds and long distances. From there your mind may run to the cosmic level of distant galaxies and space ships propelled by warp drives on a mission "to go where no one has gone before.” However, the speed of light is also important on the atomic and subatomic level. Remember that visible light is only one small section of the spectrum of electromagnetic radiation, and that ideally electrons or other particles also move at the speed of light. So, in the process of investigating the relationship between electricity and magnetism, first Michael Faraday (1791-1867) and then James Clerk Maxwell (1831-1879) developed some important equations, in which the speed of light plays an important role.
Actually, Maxwell’s equations already started to undermine some of Isaac Newton’s theories. Newton, as I have mentioned several times already, basically understood the interaction between entities in the Cartesian manner as instantaneous pushing and pulling on each other. However, Faraday and Maxwell brought a new idea into the mix: the idea that, at least in electromagnetism, there is no such thing as simultaneous interaction; any contact is “slowed down” by the speed of light. So, for example, in Newton’s system, the kinetic energy of billiard ball A is immediately transferred to billiard ball B when they collide, and there is no time lag between them. When it comes to electric charges, things don’t work that way. Let’s look at what happens when charged particles interact. The effect of one electromagnetic charge on another can be no faster than the event is communicated at the speed of light. That's pretty fast, to be sure, but it's not instantaneous.
As an illustration, imagine that someone is walking through the forest, stumbles over a root on the path, falls down, and let's out a yell for help. Fortunately, there is a boy scout nearby who can respond to the accident immediately. Well, not quite immediately. First the shout must have reached his ears, which would have taken the time necessary for it to reach him at the speed of sound. The box below is a little more accurate, and the speed of passing on a message is the speed of light.
SKIP THIS INSERT IF IT'LL GIVE YOU A HEADACHE.I am going to follow Aktins, (Physics, 438) very closely here because I really don't want to make a mistake, and I am reproducing one of his diagrams. (The anthropomorphism are mine, and I don't really believe that particles have consciousness and communicate with each other in language.) Look at the illustration below:
Find the black ball on the left, and right above it you'll see the designation "q1." q1 represents an electric charge intending to move from location A to location C by way of B. However, at location B a neutral particle is resting, and q1 slams into it. We will call the time at which this occurred t0. The path of q1 is diverted, so that q1 is now heading toward C'. Also q1 releases some electromagnetic radiation, which will affected other charges in its vicinity.
In the meantime, another charge, q2, is tooling along its own way from location D to F. Let us say that at the crucial moment t0, when q1 collides with the neutral particle, q2 is at a location that we can call E.
q2 is going to be impacted by q1's adventure, but not until the electromagnetic energy given up by q1 reaches q2. And the speed of that "communication" is c, the speed of light.
We'll give the label R to the distance that q2 traveled before receiving the message from q1. Then the time at which q2 learns of q1's collision is calculated by adding the time it took for something moving at the speed of light (c) to cover the distance R. In a formulaic expression we get: ti=t0+R/c.
So, to return to the previous topic, it became important to know to what extent the hypothetical ether might impede or accelerate the velocity of particles. The Michelson (pronounced Mikkleson)-Morley experiment seemed to demonstrate that there was no ether through which light waves needed to propagate, but physicists were slow to accept that conclusion. As mentioned in the last entry, Michelson himself never came to terms with it. Hendrik Lorentz was swayed by it after Einstein’s paper of 1905. Henri Poincaré was toying with the idea of giving it up, but there was just too much temptation to adjust other parameters rather than concede the absence of any ether, and it took him a couple of years or so to abandon it altogether.
According to a biographer, [Albrecht Fölsing, Albert Einstein (New York: Penguin, 1997)] Einstein had been wanting to find a way of getting rid of the undetectable and unproductive ether for about ten years prior to his celebrated 1905 paper “On the Electrodynamics of Moving Bodies,” which you can find in English translation as well as the original German in multiple sites on the web. If you do take the time to look at it, note how little math is involved in the first two sections that actually set up the theory. The further sections on consequences and implementations are a different story.
The problem with giving up the ether was that without it there was no longer any theoretical privileged reference point for observation of motion. As I showed in the last entry, Galilean relativity already stated that the laws of physics hold true in any inertial frame of reference, regardless of its velocity. But with the presupposition of an ether, at least one had a theoretical way of deciding the truth. Things might appear differently to different observers, but in the final analysis there was an absolute standard, as it were. If one could get a glimpse of the observed phenomenon in the ether, one would have an unimpeded picture of true reality behind the different observations. If one yanked the ether, anyone’s observations are as true as any others.
Does that sound like a relativistic epistemology to you? “Anyone’s beliefs are as true as anyone else’s.” “Nobody has a privileged vantage point from which he or she can gain absolute truth.” Well, it may sound like it, but it isn’t. I didn't say "beliefs." The discussion here is very specifically about the observation of bodies in motion, not about beliefs in general. For example, either Einstein’s theory of relativity is true, or it is not. Both points of view on this issue cannot be true. Very few people even have significant beliefs with regard to the electromagnetic properties of bodies moving at or close to the speed of light, do they? The fact that one cannot designate one of multiple observations of motion as the "true" one, does not mean that how people observe such phenomena is arbitrary or due to cultural conditioning. There is nothing capricious about how people observe things; the only limitation is that in connection with physical motion and timing they can only do so from their frame of reference.
Of course, God has an absolute frame of reference, but that’s of little help to us since we cannot share it or, for that matter, use God as our absolute frame of reference when it comes to observations in space and time. God does not have dimensions. He is without time or space (eternal and omnipresent); time and space are a part of God’s creation.
With the speed of light as a constant, certain interesting phenomena occur. Let’s say that two baseball players are riding in a convertible at 60 miles per hour (ca. 97 kilometers per hour). Just to let you know, in case you’re not familiar with baseball, a really strong pitcher may be able to throw the ball as fast as 100 mph (ca. 161 kph), but that would be a rarity. Let’s say that one of players in the car boasts that his throwing speed has been clocked at 101 mph. The other one chuckles and says that he can throw the ball a lot faster than that. He rises as much as he can in the moving vehicle and throws a ball forward in line with the direction of the car. Given the odd conditions, the throw from his arm actually only travels 85 mph, but a nearby policeman with a radar gun registers it at 145 mph. So, the ball was indeed moving a much faster velocity than that of his rival. But the pitcher really cannot take credit for it. The reason is, of course, that from the external observer’s perspective, the velocity of the ball is added to the velocity of the car: 85 mph + 60 mph = 145 mph.
The same addition of velocities will not work with speeds in the vicinity of the speed of light, however. Let us say that, instead of throwing a ball, someone in the car shines a strong flashlight ahead of the vehicle. Would that mean that an outside observer would see the flashlight emitting light at the speed of the car plus the speed of light? That is not possible. The velocity of the light beam is not c + 60 mph. It is c for an external observer just as it is for the person in the car holding the flashlight. It can get no faster than the speed of light.
Next time we’ll look at one of the first consequence of the theory of relativity: the idea that relativity supposedly makes some clocks run faster than others.
Student Bodies and Babies. Relativity is not a new idea. Nor is the idea that what we see is not necessarily what we get. Kenneth R. Atkins, the author of my undergraduate physics book, provides an amusing illustration of how we adapt to otherwise misleading perceptions(Physics, 2nd ed., New York: Wiley, 1970; orig. 1965; 459-60). He imagines that he walks into his lecture hall and realizes that 1) the students in the front row of the auditorium are about ten times the size of the ones in the back row, and 2) the university has been considerate enough to provide just the right-sized chairs, ranging from larger ones for the bigger students in the front to smaller ones for the tiny students in back. How thoughtful!
Professor Atkins tries to confirm his observation by walking to the back of the lecture hall, but realizes that his earlier observation was incomplete. The further back he moves, the more the students in the last row increase in size, while the ones in front start to shrink. He congratulates himself on having special powers that allow him to control the size of the students in his lecture room. While still in back, contemplating this unique ability, another professor walks in and lingers at the front of the auditorium. He repeats Professor Atkins' earlier observation that the students in front are larger than the ones in back. This is curious.
As the two scholars move forwards and backwards in the room and communicate with each other, Dr. Atkins has to concede that apparently his colleague has the same superpower to manipulate the size of the students. A fascinating additional consideration is that, when one of them stands in front and the other one in back, their observations should cancel out each other, but they don't. The matter is truly baffling.
After discussing the phenomenon further, the two scholars agree that the different perceptions of the students' sizes is just a matter of appearance. They are actually all roughly the same size, and if they were to establish a standard of measurement, this latter interpretation would be confirmed. In fact, given such an invention, they could express the spatial relationships with mathematical ratios and even build rules of geometry on them. However, Atkins reports, "Upon later referring to the library, we are disappointed to find that we must concede prior publication to a certain Dr. Euclid" (460).
Atkins' point is that our minds learned to adjust for visual perspective at a very early age, and so, it has become intuitive for us. The same automatic compensation could theoretically become true for people growing up with direct exposure to the results of relativity. He concludes with a dry sense of humor:
"Unfortunately, the upbringing of our children is such that they are confined to frames of reference whose relative velocities are small compared with the velocity of light. If we could take our babies and propel them through space with large variable velocities, we should presumably raise a generation to whom the results of the theory of relativity would be intuitively obvious."
I considered what that might look like, as pictured on the right, and decided that it is not likely to happen, and, thus, we will have to continue to strain our minds to comprehend some of the phenomena of relativity.
Galileo's Ark. Galileo did more than drop weights off the Tower of Pisa and look for planets around Jupiter. He also came up with the first principle of relativity, which was subsequently amplified by Isaac Newton. In the Dialogue on the Two Chief World Systems (1632), Galileo's main character, Salviati asks a group of friends to join him inside of a ship in a room with no windows (portholes). As they walk in, they notice that there are mosquitoes and butterflies in the air, and that there is a tank with some fish. He goes on to request that they would hang a leaky bucket of water from the ceiling so that its drops would fall directly into a container underneath it with a very small opening. The last favor Salviati asked for was that his visitors should jump both forward and backward. The nice thing about thought experiments or philosophy written in dialog form is that people always say and do exactly the thing that the author thinks would be appropriate. So, Salviati's guests did as requested.
Now Galileo has Salviati put the ship in motion and attain a steady cruising velocity. He and his guests once again visit the same room and nothing is changed. The insects fly as before; the fish swim around the tank with no additional trouble; the bucket still drips into the same small-mouthed container, and the people can jump back and forth the identical distances. As long as the ship maintains its velocity, everything is the same as it was without moving. The fact that the ship moves in one direction does not either increase or decrease the distances that people are able to jump. The ship represents an inertial frame of reference. Whether we use ships, automobiles, or planets revolving around the sun, the laws of physics hold true in any location from a given observer's vantage point.
What makes Galilean relativity interesting is that someone in one frame of reference may observe something different from an observer in a different frame. For example, if I sit in a moving railroad car and toss a tennis ball straight up in the air, it will come straight down to me again. But if someone were to stand at a vantage point to the side of the train and tracked the course of the ball from there, they would see it traversing a parabolic course.
This is the basic meaning of relativity. It has nothing to do with epistemological relativism except for the etymology. In fact, even in its revised form by Einstein, the whole point was to clear up the mathematical description of objects moving through space. Remember that Einstein was a Newtonian at heart, and he did not believe in any events in the universe actually occurring outside of a rigid uniformity. They might be weird, but they would obey the letter of his laws.
Let me put in a quick mention of a book and a website here. If you're fairly serious about this subject, though not necessarily intending to become a professional physicist, you may want to pick up Peter Collier, A Most Incomprehensible Thing: Notes towards a (very) gentle introduction to the mathematics of relativity. (Published by Incomprehensible Books, 2012; the location of this publisher is not given.) I think I need to state that this introduction is probably not quite as gentle as Collier hopes, but it works as long you're patient with yourself. If you are allergic to math, please stay away from it. If you do use it, or if you're working with college level math for other reasons, there are numerous websites that will be of assistance to you. Collier recommends the WolframAlpha Calculus and Analysis Calculator. I have found it to be really astounding in the range of calculations it does for you.
Ether Or Not
"Space, the final frontier ... " What exactly is "space"? I don't mean what is "outer space," but space in and of itself. Well, one might say that space is that big huge open area in which all the stuff of the universe is located, a humongous living room with virtually uncountable pieces of furniture. John Locke contended that space was infinite and paralleled eternity in God's attributes. Immanuel Kant promoted the idea that space and time are a priori forms that our minds impose on an otherwise chaotic sensory intuition. Still, for most people, space is something outside of themselves, the empty areas not occupied by other things.
But how empty can space actually be? Can you have water waves without water? Of course not. Can there be sound waves without air or some other gaseous or liquid medium? I don't think so. Can you have light waves without water, air, or some other discernible medium? Yes, apparently you can. If it were possible to construct a space with an absolute vacuum, you could still send a beam of light through it. But that doesn't seem right since waves are up-and-down pulses that move through some sort medium.
So, for centuries, right into the early twentieth century, physicists stipulated that there was a rarefied medium, called the "ether," which fills the empty spaces in the universe. Light waves are possible in the absence of any other factors because they propagate through the ether. We can't observe it or even notice it directly. It is present in all locations where there is no matter. Among various theories, the one that received the most acceptance was that the ether does not move. However, due to the constant motion of the earth (rotation around its axis and revolutions around the sun), objects moving on the earth should have to adapt to an ether wind. This stream, be it ever so light, makes a positive contribution to the speed of objects pointed in its own direction, and constitutes resistance to objects moving against it.
But how real is the ether? As solidly as its reality was embraced, it seemed to be immune from experimental testing for a long time, but by the end of the nineteenth century, experiments were forthcoming that questioned its existence. As a matter of fact, at least two other scholars were a hair's breadth away from discovering Einstein's special theory of relativity [Henri Poincaré (1854-1912) and Hendrik Lorentz (1853-1928)], but it was the fact that Einstein had liberated himself entirely from the idea of an ether that made it possible for him to make the breakthrough in a precise, non-gimmicky way. In other words he could do so without introducing some ad hoc property of the alleged ether.
The most famous experiment to refute the existence of an ether was carried out by Albert Michelson and Edward Morley in 1887. It involved splitting a beam of light and having its two halves come back together again. Since each of the two halves was now a beam in its own right, when they converged they were expected to form an interference pattern, as we mentioned earlier in connection with the double-slit experiment, and they did. If the two beams traveled along two different routes, in which one had to go counter to the direction of the ether, it should drag down its velocity somewhat and produce a different pattern than if they were both unimpeded by any resistance from the ether. No such difference was detected. I have drawn my own diagram, but please, if you're interested at all, go to the webpage where there is a professional animation put together by faculty and grad students at the University of Virginia. You can even change the settings in numerous ways and see meaningful results, including the data (here expressed in pixels per frame) you would get if a) either the speed of light were changeable, b) there were an ether moving with variable speeds, or c) if the orientation of the apparatus would make the light move in different reactions. The last part is important a) in case neither direction in the initial set-up goes directly with or against the direction of the ether, and b) since theoretically, the direction of the ether's resistance should alternate every six months.
The experiment was repeated under many different circumstances with various light sources, and the speed of light always came out identical regardless of which way the motion of the photons went. Poincaré himself later declared that the idea of the ether was a useless fiction since it contributed nothing to experimental data or predictions. Michelson, however, did not trust the experiment for which he became famous and continued to believe in the ether until the day he died.
Still, if the speed of light is truly constant, then other problems need to be addressed.
The article that almost ate my life. So, I agreed a while back to write a chapter on Hegel for an upcoming anthology on modern philosophers and theology (edited by Ben Arbour and Greg Ganssle, to be published by Zondervan some time next year I assume). After all, my Hegel website is a whole lot longer than the 6,000 word limit, and I've written a few other pieces on Hegel, not to mention my dissertation. Somehow it didn't work that easily. What do I write, and what do I leave out? After I was just about done, I hated it and started over. Then there was the question on how to handle citations. Translations of Hegel into English tend to prefer creativity and novelty over accuracy, so I obviously did my own translating. But, since I was addressing an English-reading audience, should I also refer to English translations in print so that readers could follow up, even if the translation didn't really say the same thing? Happily, I finished it this afternoon and sent it off, just a little after the deadline. It wasn't as dramatic as Hegel mailing his manuscript of the Phenomenology of Spirit past the lines of the Battle of Jena, but I'm relieved not to have to think about Hegel for a little while at least.
Last night we were treated to a massive thunderstorm along with tornado watches. It certainly was a break from the incessant snow and ice, but, then again, some warmer days without weather alerts would be welcome. This morning I was surprised that, even with all of that rain, there still was a snow cover on the ground, which goes to show how high the snow accumulation had been.
Given this preoccupation, I have not had time to put together another worthy entry on quantum mechanics and relativity, but it'll be back soon. In the meantime, you can catch up on the material so far on the cumulative web page for this topic.
Speaking of publications, congratulations to Dayton Hartmann on the publication of his first book, Joseph Smith's Tritheism (Wipf & Stock, 2014). Your humble bloggist was privileged to serve as copy editor for the author.
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v. 2: And He responded to them, “Do you think that these Galileans were more sinful than all Galileans because they suffered these things?"(HCSB)
Jesus is referring to a common phenomenon among human beings. When something bad happens to another person, we want to know why. I don't think it matters what world view people espouse, even atheism, people try to find meaning in the events of life. Bertrand Russell and Albert Camus, who protest all-too-vehemently that there is no purpose to life, are clearly confirming the rule because they know they are going against a basic intuition. It appears to me that there are two factors at work: For one thing, it's the feeling that somehow whatever people get must be what they deserved. Also, if we can find out what the person did wrong, we can reassure ourselves that we are protected against similar harm because we are not in the same category as the victims. Why do race drivers keep on going even after a close friend just got killed? As Mark Martin said in a TV interview quite a while ago (and I can only paraphrase): "We're good at rationalizing. We find out what he did, and then we tell ourselves that we wouldn't do that, and go on."
We find a good example of this attitude in the book of Job. Poor Job had lost all of his children and came down with a very painful disease. His three friends came to visit, presumably in order to cheer him up, but first they needed to reassure themselves that Job had earned his problems with some sort of sin. Job responded that he did not know of any such sin. Well, that was the wrong response as far as his "comforters" were concerned. In their opinion Job was doubling his sinfulness: first by refusing to own up to his sin and then by denying that his troubles could even be due to any sin on his part. In the end, God reproved Job's friends for their attitude.
Jesus was addressing a similar situation. The relationship between the Jews living in Galilee and Judea were not always totally harmonious. That fact, in addition to the words Jesus spoke, make it likely that there may have been a little bit of smugness in the attitude of the people who reported to Jesus about Pilate's massacre. The Galileeans in question must have deserved their fate.
It doesn't work that way. However, Jesus' statement does not go into the direction of proclaiming the innocence of those people from Galilee. All Galileans were equally sinful. Then he referred to another recent incident: eighteen people were killed when a tower around Siloah collapsed. Jesus asserted that they were no more sinful than anyone else living in Jerusalem, and no one is exempt from needing to repent.
The same truth applies to us. We are fallen creatures by birth. Our natural destiny is eternal separation from God whether we are pious and religious or practice some pagan religion or cult. But the offer of salvation through faith in Christ also goes out to everyone. As we read in Romans 6:23, eternal life is the gift of God.
It wasn't quite a heat wave, but we actually had some thawing weather. It's going to take a while for all that snow to vanish, but at least we're heading in the right direction, as far as I'm concerned.
I haven't gotten around to acknowledge a really enjoyable interview with Melissa Pellew on the talk show that she and her husband Devin host, called Theology Matters. I found it very helpful to be able to chat for a lengthy time (90 mins.), rather than be limited to two quick segments of 8 minutes between commercials, which seems to become increasingly common with some radio stations. The topic, needless to say, was my still-new book, In the Beginning God. I am finding that most of the content of the book is easy to talk about on the air, but when it comes to explaining Wilhelm Schmidt's method, it takes writing and some way of drawing diagrams.
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v. 51: Do you think that I came here to give peace to the earth? No, I tell you, but rather division! (HCSB)
Isn't it amazing how much the historical Jesus differs from many of the stereotypes of him! The emphasis is usually on his gentleness and compassion, and I'm all for that as long as we do not distort his image. We should never forget that he is the Son of God who came to earth in order to defeat evil. By implication that means that evil is real and that it needs to be defeated. But evil does not want to be defeated. The consequence is that there will be divisions among people as they encounter God's standards of righteousness and the need to trust in Christ's atonement for our sins.
That does not mean that divisiveness is a virtue. Nor does it legitimize any persecution by Christians of non-Christians, and I trust that this comment is totally superfluous. But the persecution of Christians has been a reality for the time of its existence, not only by adherents of other religions or atheists (e.g., Communists), but also by the church as an institution. In case that statement confuses you, let me just mention the execution of John Hus, who--following John Wycliffe--stood by the authority of the Bible in what was true Christian doctrine and practice. Since his conclusions were critical of several doctrines such as transubstantiation, he angered church officials from the pope on down. King Sigismund, who would become emperor a little while later, invited Hus to the Council of Constance for a debate on his views and guaranteed him safe conduct. However, the church prelates convinced Sigismund that because Hus was a heretic, he was not obligated to keep his word to such a person. Hus was imprisoned and eventually executed for his views. (There are plenty of examples from other ecclesiastical bodies as well; the story of John Hus just happens to be particularly vivid.)
Today's religious culture prides itself on highly superficial expressions of unity, which clearly cannot stand up to any serious scrutiny of the actual content of the religions. Different religions have different purposes and different means for attaining their goals (see my A Tapestry of Faiths for an in-depth discussion of these issues.) Even someone who might not be committed to the truth of any religion at all, should be able to see that one cannot mix and match religions for the sake of some contrived impression of commonality without compromising the integrity of the religions being squished together. I would not expect a member of another religion to whittle away at his beliefs just to please me, any more than I would do so to my own (though I would love for him to become a Christian).
These are serious matters. Christian apologetics (the defense of the truth of Christianity) should never be taken as some kind of intellectual entertainment. Most importantly, we must always keep in mind that the point of maintaining the truth of Christianity is not in order to win an argument, but only for the sake of other people finding salvation by the grace of God.
I really hadn't intended to write about camels. But since the topic keeps coming up, I feel that I need to state my observations on this issue (or, really non-issue). The difficulty is that it's hard to respond to something when there's really nothing to respond to, which is usually the case with an argument from silence.
Recently a National Geographic article by the Israeli journalist Mairav Zonszein has called the public's attention to the fact that archaeologists have discovered evidence of domesticated camels in the Aravah valley. This area runs along the southern part of the north-south border between Israel and Jordan. The discovery shows that the valley had been a source of copper from the 14th century into the 9th. In keeping with standard practice, the archaeologists worked through various levels of accumulated debris. They discovered that the first few levels they excavated (representing a more recent period of time) contained remnants of camels that, judging by the condition of their bones, were used to carry heavy loads of copper. But once they dug deeper than that (to more ancient times), there was no evidence of camels. More specifically, the camels first appear in the time frame between 930 and 900 BC; they remain until the mining ceased in that area about a century later.
The article does more than report this discovery. Please keep in mind that what follows was not a part of the archaeological data. Zonszein clarifies that "the biblical angle wasn't the focus of the recent research, though, just an after-the-fact observation." It would have been better if he had said, "an after-the-fact interpretation." He believes that this find constitutes evidence that domesticated camels did not exist in the Levant prior to the late 10th century BC. And thereby it raises questions that impact the veracity of the Bible.
While there are conflicting theories about when the Bible was composed, the recent research suggests it was written much later than the events it describes. This supports earlier studies that have challenged the Bible's veracity as a historic document.
Historians believe these stories took place between 2000 and 1500 B.C., based on clues such as passages from Genesis, archaeological information from the site of the great Sumerian city of Ur (located in modern Iraq), and an archive of clay tablets found at the site of Mari (in modern Syria).
Please note that Zonszein is primarily addressing the dates of the Bible's composition; he appears to accept the historicity of the patriarchs to some extent. But in his view the mention of camels in the context of Abraham's life constitutes an anachronism, and thus the truthfulness of the account as it is given in the Bible is also in doubt. Assuming that there was a "real" Abraham, he could not have kept camels.
Zonszein relates a theory on how camels first came to the Levant. Apparently they had been in use in Arabia and Egypt prior to that time. The appearance of camels at the mining site fits right around the time that Pharaoh Sheshonq I (Shishak in the Bible) invaded the kingdoms of Israel and Judah, destroying 41 towns and despoiling Solomon's treasure in Jerusalem. The article speculates: "After Egypt conquered the kingdoms of Judah and Israel, it may have reorganized the copper business and introduced camels as a more efficient means of transport than the donkeys and mules used previously." Once camels had been employed in the copper mines, their use spread rapidly, making significant contributions to the economy and culture of the Hebrews.
Herewith my responses, starting with some minor observations and moving on to hopefully more significant points:
Let me quote Sonszein's conclusion:
Archaeological excavations in the Aravah Valley have turned up bones of camels from earlier periods, perhaps even before the start of the Neolithic (about 9,700 B.C.), but those were probably wild animals that ran free, never burdened with the weight of copper ingots on their back.
It is indeed doubtful that camels would have carried massive loads of copper in the neolithic period. But to what extent they ran free is not as obvious. It is not at all clear that in these 8,000 or so years, individuals might not have domesticated camels and used them to carry lighter burdens in other areas.
So, does this issue result in a tie? Are we in a standoff because the critics have not proven that there were no domesticated camels in the area prior to 930 BC, and I have not proven that there were camels earlier than that?
Not at all. The burden of proof lies with the person disputing the veracity of a document. To say that one should not accept the truth of the biblical account until there has been independent archaeological evidence for the existence of camels at the time makes a mockery of historiography. The story of the Patriarchs includes the presence of camels. We accept the historicity of the Patriarch and, unless there is good reason to the contrary, we include the presence of camels alongside them as well. Neither the recent finds in the Aravah valley nor the arguments by Mairav Zonszein constitute sufficient reasons to the contrary. Zonszein has not made his case, and we are free to believe that Abraham's servant took his camels to the well.
In the light of a rather unfortunate set of comments in Facebook, please let me reiterate what I said at the beginning of this series, which I'm assembling at a single site as I'm moving along. My announced intention from the outset has not been to provide an exposition of quantum mechanics and relativity per se. I clearly declared my Christian perspective and that "I'm addressing an audience grounded to a certain degree in a Christian world view. Thus, this is not an apologetic directly aimed at non-Christians, but an aid to help Christians see a little more of the relationship between their faith and science." As much as anything I have two particular aims:
Even though I'm trying as hard as I can to get the physics right, the point is primarily philosophical, and, thereby, in my case, also theological. Non-Christians and atheists are certainly invited to follow, but this series is not an apologetic directed at them. I realize that contemporary atheists' feelings get hurt when they are not the center of attention, but I'm afraid that's how it is.
I had to leave off rather abruptly last night and hopefully left you in suspense concerning the debate between Einstein and Bohr at the Solvay Conferences of 1927, 1930, and 1933. A good summary is provided by the aforementioned book Entanglement by Amir D. Aczel on pp. 110-116. Einstein demonstrated a somewhat monomaniacal attitude during the time before and after sessions in coming up with thought experiments to cut defeat both the Copenhagen and the probability versions of quantum mechanics. As mentioned, typically he would come up with a potentially defeating argument; Niels Bohr would work on it all day, frequently consulting with some of the other celebrity physicists there, and come up with a sound response by dinner. But there was one time when it looked as though he was stumped.
Here's the basic principle: How much does your cat weigh? Don't try to place it on your bathroom scale; cats don't usually cooperate with such maneuvers. Instead, first weigh yourself without the cat, and then do so with it. Or vice versa. Subtract the weight-without-cat from the weight-with-cat, and you have the weight of the cat. Usually physicists make a distinction between the weight of a thing and its mass, though in this case it does not make a difference.
Einstein imagined an experiment that would supposedly disprove the uncertainty principle along similar lines. Let me try to describe it. The picture on the side was obviously made after Einstein's initial sketch, and is being circulated without attribution these days. The point of the uncertainty principle, you will remember that one cannot ascertain with certainty the momentum and location of a particle at a particular time. Keep in mind that in classical physics the momentum of an entity is understood as the product of its mass and its velocity. So,in order to ascertain the momentum, you need to know its mass, and for the velocity, you need to know the distance it covered over time. Thus, one needs an incredibly accurate clock as well. In the case of this experiment, having an accurate measure of the time and the energy are sufficient to satisfy the variables needed to satisfy a potential refutation of the uncertainty.
So Einstein posited a box filled with "excited" particles that would give off photons as they returned to a lower state of energy. At the outset, the box is weighed on an extremely precise scale. The box has a small aperture that opens briefly and immediately closes after a single photon has escaped. Now we can weigh the box again, and subtract the weight-without-photon from the weight-with-photon, and we presumably know the mass of the photon [m].
Assuming that we're working in a vacuum, we know that the photon traveled at the speed of light [c]. So we can calculate the energy of the photon with Einstein's formula E=mc2. Our super-precise clock gives us the exact time when the photon escaped. Thus we get the equivalent of what we need for the other side of the uncertainty teeter-totter.
From the contemporary accounts, Bohr was beside himself. He went from colleague to colleague trying to get their help, but no one came up with a problem in Einstein's scenario. That evening at dinner he did not have an answer. Einstein looked smug; Bohr looked harried.
However, on the next morning, instead of Einstein handing Bohr another puzzle, Bohr presented Einstein with a refutation of his thought experiment. It is based on Einstein's own general theory of relativity, which we'll come back to. Let me summarize the gist of Bohr's reasoning in my own words. How much did the box weigh before the release of the photon? Call the number x. How much does it weigh after the release? Presumably, there is a reduction in the total mass, which we can call x-Δx. The point that Bohr raised was that x did not carry the same value before and after weighing. According to Einstein's general theory of relativity, the difference in mass implies a displacement in the gravitational field, which affects the velocity of the particle (keeping in mind that velocity is a vector). And that phenomenon also entails that the clock will slow down. Consequently, the uncertainty is still there. Einstein had been defeated by use of his own theory.
Obviously, some of the numbers in this context are infinitessimal. On the other hand, the speed of light squared is a rather large quantity. Thus, what we have here is a meeting of quantum mechanics and relativity, providing a nice segue from one area to the other. We'll pursue the theories and implications of relativity as we continue the series.